69.1.56 problem 75

Internal problem ID [14209]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 75
Date solved : Tuesday, January 28, 2025 at 06:22:04 AM
CAS classification : [_exact, _rational]

\begin{align*} \frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.227 (sec). Leaf size: 37

dsolve((y(x)^2/(x-y(x))^2-1/x )+(1/y(x)-x^2/(x-y(x))^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}+\ln \left (x \right ) x -c_{1} x -x \textit {\_Z} \right )} \]

✓ Solution by Mathematica

Time used: 0.408 (sec). Leaf size: 38

DSolve[(y[x]^2/(x-y[x])^2-1/x )+(1/y[x]-x^2/(x-y[x])^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (1-\frac {1}{K[1]}\right )dK[1]+\frac {y(x)^2}{x-y(x)}+\log (x)=c_1,y(x)\right ] \]